Factor analysis of experimental design in chromatography

Summary Experimental design and factor analysis have been applied to the optimization of the separation of two series of compounds. The behavior of the nonhomogeneous series of test compounds appears to be ideal whereas the second series of congeneric substituted naphthalenes exhibit non-ideal behavior. Factor analysis maps exhibit the projection of the experiment design, on the first factorial plan, as a ternary graph for the ideal model. In this instance the linear combination of the eluents is preserved through the factor analysis projection. For the non-ideal model, the projections of the experiment design do not restore the ternary graph. Competitive interactions with ternary or quaternary eluents are clearly apparent. The simultaneous application of experimental design and factor analysis improve the optimization procedure. With the ideal model, the separation optimum can be reached directly through factor analysis maps. With the non-ideal model, the projection of eluents and their contribution to the inertia explained by the factorial axes can define a new experimental domain where maximum selectivity is obtained.Part XIV of the series Factor Analysis and Experimental Design in Chromatography. For part XIII see J. R. Chrétien, M. Righezza, A. Hassani, B. Y. Meklati,J. Chromatography,609, 261 (1992).     

Investigation of pharmaceutical high-performance liquid chromatography assay bias using experimental design

This article presents a systematic approach to investigate, document, and eliminate pharmaceutical HPLC assay bias using experimental design. This is the first article to describe the application of experimental design in the area of assay bias. It is found that both formulation and analytical variables can contribute to pharmaceutical HPLC assay bias using model compounds and formulations.     

Optimization of glucosinolate separation by micellar electrokinetic capillary chromatography using a Doehlert's experimental design

The aim of this study was to optimize by micellar electrokinetic chromatography the separation of four glucosinolates, i.e. sinigrin, glucobrassicin and methoxyglucobrassicin involved in Cruciferae resistance mechanisms and glucotropaeolin used as an internal standard. The separation borate buffer which contained sodium dodecyl sulphate, tetramethylammonium hydroxide and methanol was firstly optimized by using a three variable Doehlert experimental design. The optimum concentrations found enabled, for the first time, to obtain an acceptable resolution between the two indole glucosinolates, glucobrassicin and methoxyglucobrassicin. Modifications of the method such as a capillary pre-rinse with pure borate buffer and a step change in voltage during experiment were performed to improve the resolutions between glucosinolates and to reduce the analysis time. This method was validated by a statistical analysis and showed good linearity, repeatability and reproducibility.     

Spherical coordinate representations of solvent composition for liquid chromatography method development using experimental design

One of the major techniques used for the method development of ternary and quaternary high performance liquid chromatography (HPLC) systems has been to use mixture designs, often referred to as "Glajch's Triangle". This technique does not allow for the systematic and simultaneous optimization of other factors such as gradient time, pH and temperature that affect the quality of separations. An alternative approach is to use experimental designs. The condition, however, that the composition of all components of the mobile phase must total 100% presents a problem when trying to mathematically represent ranges of each mobile phase constituent of a ternary or quaternary system. A method is described here, based on spherical coordinate representations, that adheres to the constraints of the mobile phase composition and allows experimental designs, such as central composite and factorial designs, to be applied to the simultaneous optimization of the mobile phase composition. Other factors, in particular temperature and gradient time, can then be included in the design. As a result of applying these designs to the HPLC separation of phenols and corticosteroids, it was found necessary to include three-way interactions between experimental factors in the model. The significance of these interactions shows that they need to be considered in HPLC method development.     

Analysis of nine rhubarb anthraquinones and bianthrones by micellar electrokinetic chromatography using experimental design

An efficient micellar electrokinetic chromatography (MEKC) method has been developed for the analysis of nine anthraquinones and bianthrones in rhubarb. A chemometric approach was used to search for the optimum conditions of separation. Those factors which were found to be significant with a screening design were further optimized with a central composite face-centered (CCF) design. Acetonitrile concentration was found to be the most influential, not only in resolution, but also in analysis time and peak asymmetry. With the optimized conditions: 15 mM sodium tetraborate/15 mM sodium dihydrogenphosphate buffer, 30 mM sodium deoxycholate, pH 8.6, 17 vol.% acetonitrile and 28 kV, nine tested analytes were baseline-separated within 14 min. The method was validated to analyze the rhubarb material. Solid-phase extraction (SPE) was manipulated to remove interfering substances. Five anthraquinones and two glycosidic bianthrones were detected and quantificated. The method should be suitable for determining these major active principles in rhubarb crude drugs.     

Separation optimization of quercetin,hesperetin and chrysin in honey by micellar liquid chromatography and experimental design

The chemometrics approach was applied for the separation optimization of flavonoid markers (quercetin, hesperetin and chrysin) in honey using micellar liquid chromatography (MLC). The investigated method combines SPE of flavonoids from honey using C₁₈ cartridge and their separation and quantification by micellar liquid chromatography. A two level full factorial design was carried out to evaluate the effect of four experimental factors including concentration of SDS, alkyl chain length of the alcohol used as the organic modifier (N), volume percentage of the organic modifier (V_m) and volume percentage of acetic acid (AcOH) in mobile phase on analytes retention times. Experiments for analytes retention times modeling and optimization of separation were performed according to central composite design. Multiple linear regression method was used for the construction of the best model based on experimental retention times. Pareto optimal method was used to find suitable compatibility between resolution and analysis time of analytes in honey. The optimum mobile phase composition for separation and determination of analytes in honey were [SDS]=0.124 mol/L; 7.8% v/v ethanol and 5.0% v/v AcOH. Limits of detection and linear range of flavonoid markers were 0.0079–0.0126, 0.05–50.0 mg/L, respectively.     

Optimal design of diffusive samplers

Some commercially available diffusive samplers use two layers of adsorbent placed in series. After sampling is completed, the time weighted average concentration of analyte is estimated from the weighted sum of the uptake of analyte on these two layers. It is known that such a division into layers can increase the permissible sampling time. Here the principles underlying this sampling procedure are analyzed through a fundamental application of the theory of diffusion. Using a trial and error procedure, the optimal division of adsorbent was calculated, and the increase in sampling time that such a division can give was confirmed theoretically. Also, should the uptake in the backup layer exceed a predetermined fraction of the total uptake, this will indicate misuse of the diffusive sampler.     

Strategy for developing and optimizing liquid chromatography methods in pharmaceutical development using computer-assisted screening and Plackett-Burman experimental design

We describe a three-step method development/optimization strategy for HPLC assay/impurity methods for pharmaceuticals, which include multiple-column/mobile phase screening using a system equipped with a column-switching device, further optimization of separation by using multiple organic modifiers in the mobile phase, and multiple-factor method optimization using Plackett-Burman experimental designs. In the first two steps, commercially available chromatography optimization software, DryLab, was used to perform computer simulations. This allows the method developer to evaluate each condition (one column/mobile phase combination) with retention data from two scouting gradient runs. This approach significantly reduces the number of runs in method development. After a satisfactory separation was obtained, we used a method optimization step with Plackett-Burman experimental designs. The purpose of the 16-injection set experiments was to evaluate nine method factors with regard to method precision, accuracy, sensitivity and specificity. The results provided logical justifications in selecting method parameters such as column temperature, detection wavelength, injection volume, and sample solvent, etc. In data analysis, instead of the traditional mathematical manipulations, we used the graphical methods to examine and present data by creating the so-called main effect plots. Because replicates of design points were not run, the data did not allow the testing of statistical significance. However, it provided visual presentations in a way that is easy to understand for the method developer and end user alike.     

From experimental design to quality by design in pharmaceutical legislation

Quality by design (QbD) is a concept first outlined by Juran, who believed that quality could be planned and that most quality crises and problems relate to the way in which quality was planned in the first place. Experimental design is a powerful technique and tool for QbD, used for exploring new processes, gaining increased knowledge of the existing processes and optimizing these processes for achieving internationally competitive performance. It is also used for the investigation of relationship between parameters of ill-defined process. In this paper, the experimental design principles in pharmaceutical development and impact of these principles on pharmaceutical legislation have been reviewed. Also, slow implementation of QbD in pharmaceutical industries has been discussed. Pharmaceutical legislation is necessary for companies to continue benefiting from knowledge gained and to continually improve throughout the process lifecycle by making adaptations to assure that root causes of manufacturing problems are quickly corrected.     

Optimal conditions for the reversed-phase chromatography of proteins

Summary Optimum stationary phases for reversed phase chromatography should be based on a silica with a large average pore diameter, preferably above 30nm. To exclude anormalous elution behaviour of proteins, octadecyl groups should be bonded to the surface and the residual silanol groups should be reacted with a highly active silanization agent like bistrimethylsilyl acetamide. The total amount of bonded carbon should not exceed 5% w/w. Because of the low diffusion coefficients of proteins, the particle diameter should be as small as possible. Protein retention can hardly be influenced by changes of the organic modifier or by temperature. Because of solubility and viscosity, however, acetonitrile is to be prefered. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Analytical and experimental aspects of molecular-sieve chromatography

The object of this Review is to give analytical chemists a general introduction to molecular-sieve chromatography, a form of liquid chromatography in which molecular size forms the primary basis for separation, although other effects are also frequently involved. The technique can be used for inorganic and organic molecules, both monomeric and polymeric, in either aqueous or non-aqueous systems. The range of xerogel and aerogel molecular-sieves available at present is described, and the experimental techniques involved in their use are emphasized rather than mechanistic and theoretical considerations. The references cited have been selected critically to form a balanced, up-to-date review and also to indicate the general analytical potential and scope for future development of the technique. An Appendix lists the commercial sources of molecular-sieves and calibration standards.     

Nonlinear chromatography Recent theoretical and experimental results

The theory of nonlinear chromatography has been advanced by the incorporation of recent results obtained by the theory of partial differential equations. The system of equations of the ideal model has been solved analytically in the case of a single component for which the equilibrium isotherm between the mobile and the stationary phases is given by a Langmuir equation. A series of computer programs has been written which permits the calculation of numerical solutions of the semi-ideal model. The properties of the solutions obtained are described and discussed for a one-component system (profile of high concentration bands of a pure compound eluted by a pure solvent), several two-component systems (elution of a pure compound band by a binary mobile phase, separation of a binary mixture eluted by a pure mobile phase), and three-component systems (separation of a binary mixture eluted by a binary solvent, displacement and separation of a binary mixture). Experimental results are reported which validate the conclusions derived from the numerical integration of the model. The conclusions of the work apply to all high-performance chromatographic procedures, i.e., to those where the kinetics of mass transfer are fast enough for the mobile and stationary phases always to be near equilibrium. More specifically, the contribution from the kinetics of the retention mechanism to the mass transfer resistance must itself be negligible. This clearly excludes affinity chromatography.     

Optimal design and experimental validation of synchronous, asynchronous and flow-modulated, simulated moving-bed processes using a single-column setup

The performance of asynchronous (Varicol) and flow-modulated (PowerFeed) simulated moving-bed processes, as well as their combination into a single hybrid scheme, are studied both experimentally and by numerical simulation. A recently developed single-column experimental setup is employed to demonstrate the feasibility of the various schemes, explore the effect of their major operating parameters, and illustrate the performance enhancements that are obtained when these schemes are properly optimized. The experimental feasibility and effectiveness of the various schemes are assessed by running and comparing optimized configurations for the linear separation of two nucleosides on a high-performance reversed-phase stationary phase.     

Optimal design of affinity membrane chromatographic columns

A method for the optimal affinity membrane column design, based in the solution of the Thomas kinetic model for frontal analysis in membrane column adsorption, is presented. The method permits to choose suitable membrane operating conditions, column dimensions and processing time, to maximize the throughput when an operating capacity restriction in the range of 80–95% of the column capacity is used. Two basic design charts were obtained by computer simulation, for residence and processing time calculation, respectively. These charts can be used and manipulated in a wide range of operational conditions, provided that four design specifications related to column axial and radial Peclet numbers, length and pressure drop, are fulfilled. The application of the method was illustrated using experimental data and a simple analytical procedure. The implications of the method and results on the design and optimization of affinity membrane chromatographic columns are discussed.     

Optimization of a liquid chromatography ion mobility-mass spectrometry method for untargeted metabolomics using experimental design and multivariate data analysis

High-resolution mass spectrometry coupled with pattern recognition techniques is an established tool to perform comprehensive metabolite profiling of biological datasets. This paves the way for new, powerful and innovative diagnostic approaches in the post-genomic era and molecular medicine. However, interpreting untargeted metabolomic data requires robust, reproducible and reliable analytical methods to translate results into biologically relevant and actionable knowledge. The analyses of biological samples were developed based on ultra-high performance liquid chromatography (UHPLC) coupled to ion mobility - mass spectrometry (IM-MS). A strategy for optimizing the analytical conditions for untargeted UHPLC-IM-MS methods is proposed using an experimental design approach. Optimization experiments were conducted through a screening process designed to identify the factors that have significant effects on the selected responses (total number of peaks and number of reliable peaks). For this purpose, full and fractional factorial designs were used while partial least squares regression was used for experimental design modeling and optimization of parameter values. The total number of peaks yielded the best predictive model and is used for optimization of parameters setting.     

Void volume determination and experimental probes in reversed phase chromatography

Summary In reversed-phase liquid chromatography with n-alkyl bonded silica, the dead volume (V₀) of the column is theoretically indeterminate owing to adsorption of organic modifier on n-alkyl chains and of water on silanol groups. With binary mobile phases, retention volumes of the mobile phase components and of their deuterated species are relaeed to the adsorption isotherms and V₀ by equations which can be solved with some assumptions on the adsorbed layer composition. Methanol-water and acetonitrile-water systems are studied. As the experimental excess isotherm shows a linear part in the concentration range 50–80% in organic modifier, the hypothesis of an adsorbed layer of constant composition in this range is possible. When increasing the water content of the mobile phase, adsorption of water occurs up to saturation of silanol groups. Then the assumption of a constant water content for a mobile phase having more than 50% of water is applied. With the hypothesis of a constant adsorbed content of organic modifier when the eluent has more than 80% of organic modifier, V₀ and the absolute isotherms are calculated over the entire range of mobile phase composition. Experimental retention behavior of the mobile phase components are totally explained by these V₀ determinations. The retention times of commonly used V₀ markers are compared with V₀ values. It is shown that, when buffering the eluent, no visible effect on the distribution equilibrium is observed, so that injection of concentrated potassium nitrate is a convenient method to measure V₀. With a few solutes with are UV detectable it is possible to measure V₀ whatever the mobile phase composition in methanol-water and acetonitrile-water systems.     

A theoretical basis for parameter selection and instrument design in comprehensive size-exclusion chromatography x liquid chromatography

A novel approach for the selection of the operational parameters (linear velocity, column length) for a comprehensive 2D-LC system is discussed. Starting point for the calculations is a given second dimension ((2)D) separation and a desired peak capacity for the 2D system. Using the theory developed here the optimum settings for the first dimension ((1)D) column can be derived. Theory clearly indicates that the choice of the (1)D conditions is basically limited to just one set of column lengths and linear velocities. The new method is tested on a comprehensive two-dimensional liquid chromatography system which uses size-exclusion chromatography (SEC) followed by reversed phase liquid chromatography (RPLC). A novel LC/LC interface, using a six-port valve rather than storage loops, joins the two chromatographic dimensions. From a theoretical comparison of continuous low flow and stop-flow operation the latter method was found to be an attractive mode of interfacing. The common idea that stop-flow operation results in additional band broadening is shown to be incorrect. The new interface design operated in the stop-flow mode permits the use of conventional analytical diameter HPLC columns, 7.8mm for SEC and 4.6mm for RPLC. The reversed phase chromatography utilizes a monolithic C-18 modified silica column, which produces fast and efficient analyses. As test samples complex mixtures of peptides were analyzed.